Mist and depth render passes in Eevee are either entirely white or very little shows up
The depth pass is not normalized, so the colors represent the actual distance to your camera. The values between 0 and 1 will be represented by a grayscale gradient, but everything above 1 will be white.

In order to get a normalized output, you need to map the value in relation to the greatest value, that is to say the furthest element in your scene.

That is what the mist pass does. The values will be mapped to the [0;1] interval so it should render as grayscale.

But then, due to the interpolation which is quadratic by default, elements which are far from the camera will be so close to the upper bound that they will be unrecognizable from the pure white value.

You can change the default distances in the world settings, under the Mist Pass panel :



A solution is to restrict the range, not to [0,1] but to [0,x] where x is a value you can tweak with a math divide node.